License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2021.22
URN: urn:nbn:de:0030-drops-139177
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13917/
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Holub, Štěpán ; Starosta, Štěpán

Formalization of Basic Combinatorics on Words

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LIPIcs-ITP-2021-22.pdf (1 MB)


Abstract

Combinatorics on Words is a rather young domain encompassing the study of words and formal languages. An archetypal example of a task in Combinatorics on Words is to solve the equation x ⋅ y = y ⋅ x, i.e., to describe words that commute.
This contribution contains formalization of three important classical results in Isabelle/HOL. Namely i) the Periodicity Lemma (a.k.a. the theorem of Fine and Wilf), including a construction of a word proving its optimality; ii) the solution of the equation x^a ⋅ y^b = z^c with 2 ≤ a,b,c, known as the Lyndon-Schützenberger Equation; and iii) the Graph Lemma, which yields a generic upper bound on the rank of a solution of a system of equations.
The formalization of those results is based on an evolving toolkit of several hundred auxiliary results which provide for smooth reasoning within more complex tasks.

BibTeX - Entry

@InProceedings{holub_et_al:LIPIcs.ITP.2021.22,
  author =	{Holub, \v{S}t\v{e}p\'{a}n and Starosta, \v{S}t\v{e}p\'{a}n},
  title =	{{Formalization of Basic Combinatorics on Words}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13917},
  URN =		{urn:nbn:de:0030-drops-139177},
  doi =		{10.4230/LIPIcs.ITP.2021.22},
  annote =	{Keywords: combinatorics on words, formalization, Isabelle/HOL}
}

Keywords: combinatorics on words, formalization, Isabelle/HOL
Collection: 12th International Conference on Interactive Theorem Proving (ITP 2021)
Issue Date: 2021
Date of publication: 21.06.2021
Supplementary Material: Software (Code Repository): https://gitlab.com/formalcow/combinatorics-on-words-formalized archived at: https://archive.softwareheritage.org/swh:1:dir:78c9955742137e63eb137885a27acfd231a576f5


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